Eddington Publishes

Arthur Stanley Eddington’s pioneering contribution to astronomy and astrophysics, set forth in The Internal Constitution of the Stars, spanned the most important aspects of stellar structure constitution and evolution.

Summary of Event

At the beginning of the twentieth century, astrophysical knowledge was at best only rudimentary. The source of stellar energy had not yet been discovered. Although scientists understood the proper motions of the stars—that is, the sum of radial and transverse velocities—William Herschel’s Herschel, William assumption of their randomness relative to the Sun had been abandoned by Jacobus Cornelius Kapteyn Kapteyn, Jacobus Cornelius on the basis of his pioneering study of the subject. At this stage, Karl Schwarzschild Schwarzschild, Karl attempted to represent the radial velocity vectors of the stars as forming an ellipsoid. Kapteyn, however, noted that they formed, instead, a double-lobed curve. [kw]Eddington Publishes The Internal Constitution of the Stars (July, 1926)
[kw]Publishes The Internal Constitution of the Stars, Eddington (July, 1926)
[kw]Internal Constitution of the Stars, Eddington Publishes The (July, 1926)
[kw]Stars, Eddington Publishes The Internal Constitution of the (July, 1926)
Internal Constitution of the Stars, The (Eddington)
Stellar evolution
[g]England;July, 1926: Eddington Publishes The Internal Constitution of the Stars[06670]
[c]Science and technology;July, 1926: Eddington Publishes The Internal Constitution of the Stars[06670]
[c]Astronomy;July, 1926: Eddington Publishes The Internal Constitution of the Stars[06670]
Eddington, Arthur Stanley
Adams, Walter Sydney
Fowler, Ralph H.
Pease, Francis Gladheim
Anderson, John August
Kramers, Hendrik Anthony
Bethe, Hans Albrecht

In 1906, Sir Arthur Stanley Eddington, investigating proper motions of stars, was able to isolate two star streams, or drifts. He confirmed the above-mentioned facts through a statistical analysis of the proper motion data. During these early years, Eddington studied problems associated with the distribution of stars of different spectral class, planetary nebulas, open clusters, and the dynamics of globular clusters.

Eddington’s pioneering work in astrophysics began in 1916. A decade earlier, Ralph Allen Sampson Sampson, Ralph Allen had pointed out the importance of radiation pressure in the physics of stars, and Schwarzschild later developed a theory of radiative equilibrium for the stellar atmospheres. Eddington, realizing the important role the radiation pressure played in maintaining the equilibrium in massive stars, extended Schwarzschild’s theory all the way to the stellar core. Utilizing Robert Emden’s differential equation for a polytropic sphere with index n = 3, assuming that the materials of a giant star behave like a perfect gas, and accounting for gravitational force, gas pressure, and radiation pressure, he developed the well-known equation of radiative equilibrium. Known as Eddington’s model of a star, it was found to be applicable to white dwarfs as well. White dwarf stars

It was known that matter inside a star would be highly ionized because of extreme temperature. Incorporating this fact into his theory of stellar equilibrium, Eddington showed that high ionization reduced the molecular weight of a gas by two for all elements except hydrogen. Radiation pressure was found to increase rapidly with rising stellar mass, resulting in instabilities; hence Eddington concluded that the number of stars in excess of ten solar masses would be rare.

The derivation of mass-luminosity relation of a star requires knowledge of fundamental processes contributing to stellar opacity. After the photoelectric absorption process, regarded as dominant, met with criticism, Eddington, employing Hendrik Anthony Kramers’s theory of absorption coefficients and introducing his so-called guillotine factor, obtained the important mass-luminosity relationship. Mass-luminosity relationship of stars[Mass luminosity relationship] Moreover, having realized that electron scattering is the major source of stellar opacity, he was able to derive an upper limit to luminosity for a given mass—“Eddington’s limit” Eddington’s limit[Eddingtons limit] —which plays an important role in the investigation of X-ray sources and accretion discs around black holes. Based on the fact that the observed luminosity data fit well with his theoretical computation, Eddington concluded that both giant Giant stars and dwarf stars Dwarf stars were gaseous, even though the latter had exceedingly high density.

Eddington’s computation on the basis of his theory of stellar constitution of angular diameters of several giant stars—including Betelgeuse, Antares, and Aldebaran—was confirmed observationally by Francis Gladheim Pease and John August Anderson at Mount Wilson Observatory in California. Applying his theory to the dwarf star Sirius B, Sirius B (star) Eddington noted to his astonishment that the mass density of the star was 50 million kilograms (approximately 55,116 tons) per cubic meter. He realized that such a dense star should exhibit measurable gravitational redshift in accordance with Einstein’s relativity theory, and he had Walter Sydney Adams at Mount Wilson successfully verify this effect. Having established the diameter of Sirius B to be 38 million meters (about 23,612 miles), comparable to that of Earth, Eddington found its density to be 53 million kilograms (58,422 tons) per cubic meter. Ralph H. Fowler, employing Erwin Schrödinger’s wave mechanics, formulated the theory of degenerate dense matter found in stars such as Sirius B.

A problem of great complexity that resulted in Eddington’s interest in the internal constitution of stars and occupied his attention for a long time is associated with the Cepheid variable. Cepheid variable stars Luminosities of these bright F and G stars vary with a periodicity ranging from a day to several weeks. After generalizing Johann Wilhelm Ritter’s analysis of the adiabatic pulsation of a gaseous star in convective equilibrium to the case of a star in radiative equilibrium, Eddington was able to combine the result with the mass-luminosity formulism, so as generally to obtain period-luminosity relations of Cepheids. Although these earlier attempts did not agree with correct phase relations among the observed variables such as brightness and temperature, Eddington realized that one had to examine the problem of energy transfer more thoroughly and returned to it several times. He was able to establish that the longer the periodicity of a star, the lower its surface temperature. With his pulsation theory, Eddington laid the foundation for future work on the Cepheids.

In addition to covering his research for a time span of ten years, beginning in 1916, Eddington’s The Internal Constitution of the Stars also contains chapters devoted to stellar surface, chromosphere, atmosphere, and abundance of elements. His speculative prediction about the source of stellar energy appears in one of his papers. Twenty years later, Hans Albrecht Bethe showed that within the dense, hot core of a star, four protons would combine to form a helium atom via the carbon-nitrogen-carbon cycle so that a small fraction of the mass would be converted into radiant energy. This is one of the possible sources of stellar energy. Eddington was keenly aware that the source of the star’s energy must be deep within the core.

While involved with the major projects, Eddington investigated the problem of cosmic abundance of hydrogen and the central temperature and density of stars. His theory of absorption lines of stellar atmosphere made it possible to interpret many observed spectral line intensities. His theory concerning the temperature, density, and composition of interstellar matter and its emission and absorption properties of light provided an independent rough measurement of distances.


Eddington wrote more than 150 scientific articles and more than a dozen books. His profound knowledge of mathematics, deep intuitive insight into natural problems, and unrelenting drive enabled him to delve into a wide range of topics. His pioneering contributions to astronomy and astrophysics are distilled in his classic masterpiece The Internal Constitution of the Stars. It would not be an overstatement to say that the publication of his work opened up a new and exciting vista of astronomy and astrophysics. Even while Eddington’s research work was being published, the stimulus it provided was evident from the immediate and long-lived controversy it generated among leading researchers in the field of astrophysics, such as James Hopwood Jeans and Edward Arthur Milne.

The publication of The Internal Constitution of the Stars established Eddington firmly as the founder of modern theoretical astrophysics and provided pathways to the study of structure, constitution, and evolution of stars. Several aspects of investigations of stellar structure—pioneered by Eddington and treated in his book—were pursued by others, leading to successful conclusions. Eddington’s search for a theory to explain the periodicity of Cepheid variables, one of his earliest research interests, occupied him for a substantial period of his life. The problem of the Cepheids was ultimately solved by Martin Schwarzschild, Paul Ledoux, and Robert Frederick Christy. His speculations and predictions in regard to stellar energy turned out to be an important initial step, leading Bethe and others to elegant solutions. Eddington’s study of the effects of reflection in binaries for determining their masses served later as a prototype solution to problems of diffuse reflection and transmission of light.

Eddington’s investigation of interstellar absorption of lines led to dual results: determination of relative abundance of elements by the method of the “curve of growth,” developed by Albrecht Otto, Johannes Unsold, and Marcel Gilles Minnaert, as well as prediction of radial velocities and, hence, approximation of distances, confirmed by Otto Struve and John Stanley Plaskett. Eddington’s deduction of the size and ultrahigh density of dwarf stars, followed by Fowler’s theory of degenerate matter, later led Subrahmanyan Chandrasekhar to deduce an upper limit to masses of such stars, which is known as the Chandrasekhar limit. Eddington’s contributions to astrophysics thus spanned the most important aspects of stellar structure. As Milne noted in 1945, Eddington “brought it all to life, infusing it with his sense of real physics and endowing it with aspects of splendid beauty. . . . Eddington will always be our incomparable pioneer.” Internal Constitution of the Stars, The (Eddington)
Stellar evolution

Further Reading

  • Chandrasekhar, Subrahmanyan. Eddington: The Most Distinguished Astrophysicist of His Time. Cambridge, England: Cambridge University Press, 1983. Presents two Sir Arthur Stanley Eddington Centenary Lectures delivered by Chandrasekhar at Trinity College, the University of Cambridge, in late 1982. Valuable source offers a cameo view of the life and achievements of Eddington by a great astrophysicist of modern times.
  • Douglas, A. Vibert. The Life of Arthur Stanley Eddington. London: Thomas Nelson & Sons, 1957. This biography includes a complete list of Eddington’s scientific papers and books, in addition to a genealogical table. The volume reads like a novel and is comprehensive in every respect, embodying all aspects of Eddington’s life and scientific achievements. The text may serve even as an excellent primer for stellar structure, relativity, and the philosophy of science.
  • Eddington, Arthur Stanley. The Internal Constitution of the Stars. 1926. Reprint. Mineola, N.Y.: Dover, 1959. Eddington’s celebrated work is written in a style accessible to general readers. Many of the arguments presented are easy to understand; readers with some college-level background in astronomy should be able to absorb the work in its entirety. Includes references.
  • _______. Stellar Movements and the Structure of the Universe. London: Macmillan, 1914. Presents Eddington’s statistical analysis of data on the proper motion of stars, distribution of stars based on their spectral class, planetary nebulas, and star clusters, published in about fifteen papers, in addition to the cosmological knowledge of the period. Aimed at general readers of scientific literature. Provides a background for understanding Eddington’s later work on stellar structure.
  • Miller, Arthur I. Empire of the Stars: Obsession, Friendship, and Betrayal in the Quest for Black Holes. Boston: Houghton Mifflin, 2005. Provides background on the history of the idea of black holes and describes the debate between Chandrasekhar and Eddington concerning the nature of black holes as well as the implications of that debate for twentieth century science.
  • Motz, Lloyd, and Jefferson Hane Weaver. The Story of Astronomy. New York: Plenum, 1995. Presents the history of astronomy from ancient times to the end of the twentieth century. Chapter 15 discusses Eddington’s work in the context of the beginnings of astrophysics. Includes bibliography and index.
  • Struve, Otto, and Velta Zebergs. Astronomy of the Twentieth Century. New York: Macmillan, 1962. Excellent survey for the general reader includes discussion of stellar properties and mass determination for binary stars. Features drawings, black-and-white photographs, and diagrams as well as glossary and bibliography.

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